Thermal stability and the behaviour in organic solvents of some poly(ester-siloxane)urethanes

Three new chemically crosslinked polyurethanes were synthesized. Their behaviour in organic solvents and in dynamic heating conditions was studied. Predictions regarding the thermal stability have been made by using the isoconversion kinetic method.     

Quasi-Baer module hulls and applications

Let V be a module with $S=\mathrm{End}(V)$. V is called a quasi-Baer module if for each ideal J of S, $r_V(J)=eV$ for some $e^2=e\in S$. On the other hand, V is called a Rickart module if for each $?\in S$, $\mathrm{Ker}(?)=eV$ for some $e^2=e\in S$. For a module N, the quasi-Baer module hull $\mathbf{qB}(N)$ (resp., the Rickart module hull $\mathbf{Ric}(N)$) of N, if it exists, is the smallest quasi-Baer (resp., Rickart) overmodule, in a fixed injective hull $E(N)$ of N. In this paper, we initiate the study of quasi-Baer and Rickart module hulls. When a ring R is semiprime and ideal intrinsic over its center, it is shown that every finitely generated projective R-module has a quasi-Baer hull. Let R be a Dedekind domain with F its field of fractions and let $\{K_i|i\in \mathrm{\Lambda }\}$ be any set of R-submodules of $F_R$. For an R-module $M_R$ with ${\mathrm{Ann}}_R(M)\ne 0$, we show that $M_R\oplus {({?}_{i\in \mathrm{\Lambda }}{K}_i)}_R$ has a quasi-Baer module hull if and only if $M_R$ is semisimple. This quasi-Baer hull is explicitly described. An example such that $M_R\oplus {({?}_{i\in \mathrm{\Lambda }}{K}_i)}_R$ has no Rickart module hull is constructed. If N is a module over a Dedekind domain for which $N/t(N)$ is projective and ${\mathrm{Ann}}_R(t(N))\ne 0$, where $t(N)$ is the torsion submodule of N, we show that the quasi-Baer hull $\mathbf{qB}(N)$ of N exists if and only if $t(N)$ is semisimple. We prove that the Rickart module hull also exists for such modules N. Furthermore, we provide explicit constructions of $\mathbf{qB}(N)$ and $\mathbf{Ric}(N)$ and show that in this situation these two hulls coincide. Among applications, it is shown that if N is a finitely generated module over a Dedekind domain, then N is quasi-Baer if and only if N is Rickart if and only if N is Baer if and only if N is semisimple or torsion-free. For a direct sum $N_R$ of finitely generated modules, where R is a Dedekind domain, we show that N is quasi-Baer if and only if N is Rickart if and only if N is semisimple or torsion-free. Examples exhibiting differences between the notions of a Baer hull, a quasi-Baer hull, and a Rickart hull of a module are presented. Various explicit examples illustrating our results are constructed.     

Parallel distributed-memory simplex for large-scale stochastic LP problems

We present a parallelization of the revised simplex method for large extensive forms of two-stage stochastic linear programming (LP) problems. These problems have been considered too large to solve with the simplex method; instead, decomposition approaches based on Benders decomposition or, more recently, interior-point methods are generally used. However, these approaches do not provide optimal basic solutions, which allow for efficient hot-starts (e.g., in a branch-and-bound context) and can provide important sensitivity information. Our approach exploits the dual block-angular structure of these problems inside the linear algebra of the revised simplex method in a manner suitable for high-performance distributed-memory clusters or supercomputers. While this paper focuses on stochastic LPs, the work is applicable to all problems with a dual block-angular structure. Our implementation is competitive in serial with highly efficient sparsity-exploiting simplex codes and achieves significant relative speed-ups when run in parallel. Additionally, very large problems with hundreds of millions of variables have been successfully solved to optimality. This is the largest-scale parallel sparsity-exploiting revised simplex implementation that has been developed to date and the first truly distributed solver. It is built on novel analysis of the linear algebra for dual block-angular LP problems when solved by using the revised simplex method and a novel parallel scheme for applying product-form updates.     

𝔏-Rickart Modules

It is well known that the Rickart property of rings is not a left-right symmetric property. We extend the notion of the left Rickart property of rings to a general module theoretic setting and define 𝔏-Rickart modules. We study this notion for a right R-module M _R where R is any ring and obtain its basic properties. While it is known that the endomorphism ring of a Rickart module is a right Rickart ring, we show that the endomorphism ring of an 𝔏-Rickart module is not a left Rickart ring in general. If M _R is a finitely generated 𝔏-Rickart module, we prove that End _R (M) is a left Rickart ring. We prove that an 𝔏-Rickart module with no set of infinitely many nonzero orthogonal idempotents in its endomorphism ring is a Baer module. 𝔏-Rickart modules are shown to satisfy a certain kind of nonsingularity which we term “endo-nonsingularity.” Among other results, we prove that M is endo-nonsingular and End _R (M) is a left extending ring iff M is a Baer module and End _R (M) is left cononsingular.     

Selective dissolution of TiO2 crystalline phases: Physicochemical characterization and photocatalytic activity

In this study, different commercially available TiO₂ powders (Degussa P25, pure anatase, and rutile) were submitted to selective dissolution treatments, with H₂O₂/NH₄OH and 10% HF, known to remove rutile and anatase from physical mixtures. The aim was to check whether a particular separation method designed to remove a specific crystalline phase influences the properties of the other phase from the mixture or not. More precisely, we have studied how the HF dissolution method designed to selectively remove the anatase affected the physicochemical and photocatalytic properties of rutile. In a similar way, the changes in the anatase properties were studied, after the H₂O₂/NH₄OH treatment, initially used to remove rutile from the mixture. All the samples were characterized by X-ray diffraction, nitrogen adsorption–desorption, transmission electron microscopy, diffuse reflectance (DR) ultraviolet–visible, and Raman spectroscopy. The photocatalytic activity of these powders was tested in the oxidation of p-chlorophenol from water. The selective treatment methods not only dissolved the target phase but also changed some physicochemical and the photocatalytic performances of the other TiO₂ crystalline phase in a considerable manner. These aspects should be taken into account in the studies regarding the synergistic effects of anatase and rutile, especially in reconstructed TiO₂ photocatalysts.     

Squaraine Dyes: Interaction with Bovine Serum Albumin to Investigate Supramolecular Adducts with Aggregation‐Induced Emission (AIE) Properties

Bovine serum albumin (BSA)–squaraine supramolecular adducts with aggregation‐induced emission (AIE) properties were prepared and characterized by spectroscopic methods. While squaraine dyes showed a very low fluorescence quantum yield in water, a great enhancement in the fluorescence of the aggregated BSA adducts was achieved due to the abnormal aggregation‐induced emission properties of squaraines. The adducts formation was studied from a kinetic point of view showing unexpected structure–properties relationships.     

Polyaniline “Nanotube” Self‐Assembly: The Stage of Granular Agglomeration on Nanorod Templates

The identification and control of a critical stage of polyaniline “nanotube” self‐assembly is presented, namely the granular agglomeration or growth onto nanorod templates. When the synthesis pH is held above 2.5, smooth insulating nanorods exhibiting hydrogen bonding and containing phenazine structures are produced, while below pH 2.5, small 15–30 nm granular polyaniline nanoparticles appear to agglomerate onto the available nanorod surface, apparently improving conductivity of the resulting structures by three orders of magnitude. This finding affects both fundamental theories of polyaniline nanostructure self‐assembly and their practical applications.